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A292443
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a(n) = (5/32)*A000045(6*n)^2.
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2
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0, 10, 3240, 1043290, 335936160, 108170400250, 34830532944360, 11215323437683690, 3611299316401203840, 1162827164557749952810, 374426735688279083601000, 120564246064461307169569210, 38821312806020852629517684640, 12500342159292650085397524884890
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OFFSET
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0,2
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COMMENTS
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Every term is a triangular number. [Problem B-967 in Euler and Sadek, 2003; solution in Euler and Sadek, 2004]
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LINKS
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FORMULA
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G.f.: 10*x*(1 + x) / ((1 - x)*(1 - 322*x + x^2)).
a(n) = ((161+72*sqrt(5))^(-n)*(-1+(161+72*sqrt(5))^n)^2) / 32.
a(n) = 323*a(n-1) - 323*a(n-2) + a(n-3) for n > 2.
(End)
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MATHEMATICA
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PROG
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(PARI) a(n) = (5/32)*fibonacci(6*n)^2
(Magma) [5*Fibonacci(6*n)^2/32: n in [0..20]]; // G. C. Greubel, Feb 03 2019
(Sage) [5*fibonacci(6*n)^2/32 for n in (0..20)] # G. C. Greubel, Feb 03 2019
(GAP) List([0..20], n-> 5*Fibonacci(6*n)^2/32) # G. C. Greubel, Feb 03 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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